Automating the Selection of Proxy Variables of Unmeasured Confounders

TL;DR

This paper develops methods to automatically identify valid proxy variables for unmeasured confounders in causal inference, enabling unbiased estimation of treatment effects without prior knowledge of proxy validity.

Contribution

It extends existing proxy variable estimators to multiple confounders and introduces data-driven selection methods based on statistical properties.

Findings

Effective identification of proxy variables demonstrated on synthetic data.

Accurate causal effect estimation shown on real-world datasets.

Theoretical guarantees support the proposed algorithms.

Abstract

Recently, interest has grown in the use of proxy variables of unobserved confounding for inferring the causal effect in the presence of unmeasured confounders from observational data. One difficulty inhibiting the practical use is finding valid proxy variables of unobserved confounding to a target causal effect of interest. These proxy variables are typically justified by background knowledge. In this paper, we investigate the estimation of causal effects among multiple treatments and a single outcome, all of which are affected by unmeasured confounders, within a linear causal model, without prior knowledge of the validity of proxy variables. To be more specific, we first extend the existing proxy variable estimator, originally addressing a single unmeasured confounder, to accommodate scenarios where multiple unmeasured confounders exist between the treatments and the outcome. Subsequently, we present two different sets of precise identifiability conditions for selecting valid proxy variables of unmeasured confounders, based on the second-order statistics and higher-order statistics of the data, respectively. Moreover, we propose two data-driven methods for the selection of proxy variables and for the unbiased estimation of causal effects. Theoretical analysis demonstrates the correctness of our proposed algorithms. Experimental results on both synthetic and real-world data show the effectiveness of the proposed approach.